Question

若在二項(xiàng)式(x+1)ⁿ(n＞3且n∈N^*)的展開式中任取一項(xiàng),該項(xiàng)的系數(shù)為奇數(shù)的概率是1,則在二項(xiàng)式(x+1)^n-1的展開式中任取一項(xiàng),該項(xiàng)的系數(shù)為奇數(shù)的概率是p,為偶數(shù)的概率是q,那么p-q=______________.

Answer 1

  由題意(x+1)ⁿ的展開式的每一項(xiàng)的系數(shù)都是奇數(shù),共有n+1項(xiàng),則(x+1)^n-1的展開式共有n項(xiàng),且有個(gè)系數(shù)為奇數(shù)的項(xiàng),有個(gè)系數(shù)為偶數(shù)的項(xiàng)(n為奇數(shù)).

∴p==,q=.∴p-q=.